Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(\cos x)^{\cos x}$ Solution:...
Read More →A block of mass $m$ and having a charge q is placed
Question: A block of mass $m$ and having a charge $q$ is placed on a smooth horizontal table and is connected to a wall through an unstressed spring of spring constant $k$ as shown in figure (29.E1). A horizontal electric field E parallel to the spring is switched on. Find the amplitude of the resulting SHM of the block. Solution:...
Read More →The bob of a simple pendulum has a mass of
Question: The bob of a simple pendulum has a mass of $40 \mathrm{~g}$ and a positive charge of $4.0 \times 10^{-6} \mathrm{C}$. It makes 20 oscillations in $45 \mathrm{~s}$. A vertical electric field pointing upward and of magnitude $2.5^{\times 10^{4}} \mathrm{~N} / \mathrm{C}$ is switched on. How much time will it now take to complete 20 oscillations? Solution:...
Read More →A ball of mass 100g and having a charge of
Question: A ball of mass $100 \mathrm{~g}$ and having a charge of $4.9^{\times 10^{-5}} \mathrm{C}$ is released from rest in a region where a horizontal electric filed of $2.0^{\times 10^{4}} \mathrm{~N} / \mathrm{C}$ exists. (a) Find the resultant force acting on the ball. (b) What will be the path of the ball? (c) Where will the ball be at the end of $2 \mathrm{~s}$ ? Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(\tan x)^{\sin x}$ Solution:...
Read More →Three identical charges, each having a value
Question: Three identical charges, each having a value $1.0^{-8} 10^{-8} \mathrm{~V}$, are placed at the corners of an equilateral triangle of side $20 \mathrm{~cm}$. Find the electric field and potential at the center of the triangle. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(\cos x)^{\log x}$ Solution:...
Read More →A water particle of mass 10.0mg and having a charge of
Question: A water particle of mass $10.0 \mathrm{mg}$ and having a charge of $1.50 \times 10^{-6} \mathrm{C}$ stays suspended in a room. What is the magnitude of electric field in the room? What is its direction? Solution:...
Read More →A point charge produces an electric an electric field
Question: A point charge produces an electric an electric field of magnitude $5.0 \mathrm{~N} / \mathrm{C}$ at a distance of $40 \mathrm{~cm}$ from it. What is the magnitude of the charge? Solution:...
Read More →Two particles A and B having charges of
Question: Two particles $A$ and $B$ having charges of $+2.00^{-6} \times 10^{-6} \mathrm{C}$ and of $-4.00^{-6} \times 10^{-6}$ Crespectively are held fixed at a separation of $20.0 \mathrm{~cm}$. Locate the point(s) on the line AB where (a) the electic field is zero (b) The electric potential is zero. Solution:...
Read More →The electric force experienced by a charge of
Question: The electric force experienced by a charge of $1.0^{\times 10^{-6}} \mathrm{c}$ is $1.5^{\times 10^{-3}} \mathrm{~N}$. Find the magnitude of the electric at the position of the charge. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when:. $y=(\log x)^{\sin x}$ Solution:...
Read More →Repeat the previous problem if the particle C is displaced
Question: Repeat the previous problem if the particle $C$ is displaced through a distance $x$ along the line $A B$. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(\sin x)^{\cos x}$ Solution:...
Read More →Two particles A and B, each carrying a charge Q are held fixed
Question: Two particles $A$ and $B$, each carrying a charge $Q$ are held fixed with a separation $d$ between them. A particle $C$ having mass $m$ and charge $q$ is kept at the middle point of the line $A B$. (a) If it is displaced through a distance $x$ perpendicular to $\mathrm{AB}$, what would be the electric force experienced by it. (b) Assuming $xd$, show that this force is proportional to $x$. (c) Under what condition will the particle C execute simple harmonic motion if it is released afte...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(\tan x)^{1 / x}$ Solution:...
Read More →Two particles A and B,
Question: Two particles $A$ and $B$, each having a charge $Q$, are placed a distance $d$ apart. Where should a particle of charge $q$ be placed on the perpendicular bisector of $A B$ so that it experiences maximum force? What is the magnitude of this maximum force? Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=x^{\left(\cos ^{-1} x\right)}$ Solution: Here, we need to take log both the sides to get that differentiation simple....
Read More →A particle having a charge of
Question: A particle having a charge of $2.0^{\times 10^{-6}} \mathrm{C}$ and a mass of $100 \mathrm{~g}$ is placed at tom of a smooth inclined plane of inclination $30^{\circ}$ Where should another particle B, having same charge and mass, be placed on the incline so that it may remain in equilibrium? Solution:...
Read More →A particle A having a charge of
Question: A particle A having a charge of $2.0^{\times 10^{-6}} \mathrm{C}$ is held fixed on a horizontal table. A second charged particle of mass $80 \mathrm{~g}$ stays in equilibrium on the table at a distance of $10 \mathrm{~cm}$ from the first charge. The coefficient of friction between the table and this second particle is ${ }^{\mu}=0.2$. Find the range within which the charge of this second particle may lie. Solution:...
Read More →Two identically charged particles are fastened to the two rnds of
Question: Two identically charged particles are fastened to the two rnds of a spring of spring constant . $100 \mathrm{~N} / \mathrm{m}$ and natural length $10 \mathrm{~cm}$. the system rests on a smooth horizontal table. If the charge on each particle is $2.0 \times 10^{-8} \mathrm{C}$, find the extension in the length of the spring. Assume that the extension is small as compared to the natural length. Justify this assumption after you solve the problem. Solution:...
Read More →Two particles A and B having charges q and 2q respectively
Question: Two particles $\mathrm{A}$ and $\mathrm{B}$ having charges $\mathrm{q}$ and $2 \mathrm{q}$ respectively are placed on a smooth table with a separation d. A third particle $\mathrm{C}$ is to be clamped on the table in such a way that the particles $\mathrm{A}$ and $\mathrm{B}$ remain at rest on the table under electrical forces. What should be the charge on $C$ and where should it be clamped? Solution:...
Read More →A particle having a charge of
Question: A particle having a charge of $\times 10^{-4} \mathrm{C}$ is placed directly below and at a separation of $10 \mathrm{~cm}$ from the bob of a simple pendulum at rest. The mass of the bob is $100 \mathrm{~g}$, what charge should the bob be given so that the string becomes loose. Solution:...
Read More →Two identical pith balls, each carrying a charge q,
Question: Two identical pith balls, each carrying a charge q, are suspended from a common point by two strings of equal length I. Find the mass of each ball if the angle between the strings is $2 \theta$ in equilibrium. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=x^{\sin x}$ Solution:...
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